In a gas turbogenerator set of the prior art, with a downstream recuperator for utilizing the heat of the exhaust gases from a turbine belonging to the gas turbogenerator set, it can generally be found that the heat yield from the still relatively hot exhaust gases is deficient, with the result that flue gases, the temperature of which may well still amount to 250.degree. C., are discharged. This situation is aggravated in sequentially fired gas turbogenerator sets, since, in these, only about 60% of the available compressed air can be passed through the recuperator. By contrast, the recuperator is subjected to exhaust gas to the extent of about 103%, so that it can easily be seen from this that only some of the heat potential of these exhaust gases can be utilized. In order to seek a remedy for this, it has become known to place a second recuperator downstream of the first: by means of this measure, the remaining heat potential of the exhaust gases is to be utilized even further here, preferably by attempts to provide a steam quantity which is then introduced into a steam turbine. However, high-grade steam cannot be provided in this way, so that such a measure results per se in a high loss of exergy.